Every year numerous multi-purpose sports arenas are built around the world. These stadia are often covered for weather protection, climate control, and acoustic control of the inside environment. The large maintenance costs of existing fabric and steel structures as well as the ever increasing construction costs of these stadia have created a need for the development of efficient structural systems that can reduce the weight of the overall cover, reduce the loads on the support structure or other foundation, shorten the construction time, integrate with roof or closure arrangements rather than merely support them, reduce the maintenance costs over the life of the structure, and reduce the construction cost of the structure.
Single network geodesic domes with up to 420 ft spans have been designed and constructed using extruded aluminum beams. Such a single network geodesic dome is described in the context of U.S. Pat. No. 3,909,994 to Richter which is incorporated herein by reference. The proven advantages of the use of aluminum in large span construction have enabled aluminum domes to compete successfully against steel, wood, and fabric domes. The advantages of aluminum construction include its light weight, corrosion resistance, ease of manufacturing, reduced maintenance, and high strength to weight ratio.
The basic contour of the surface of a dome, apart from local features of the surface, usually is a portion of a surface of revolution, such as a portion of a sphere, cylinder, ellipsoid, as examples. Other kinds of surface contours have been and can be used.
An approach to the structural design of a dome is to use a single network of structural members, or struts, which are located in and define the dome's basic contour surface and which are interconnected to subdivide that surface into a lattice of triangular, rectangular, pentagonal, hexagonal or other polygonal areas. The lattice area shape is exclusively or predominantly, in most instances, that of one kind of polygon. The construction of that structural network is simplest when all of the struts in the network are of uniform cross-section. From a buckling point of view, for typical live loads or snow loads the dome areas most susceptible to failure are its central areas. In the dome central region, loads are applied normal to the struts and cause those struts to buckle more readily than at the perimeter of the dome where the struts are more vertically oriented and form an acute angle relative to the applied loads.
If struts of depth and cross-sectional area adequate to carry central region loads are used throughout the dome, substantial portions of the dome will be over-designed. The dome will be heavier and more costly than truly required. If the use of stronger/deeper structural members is confined to the portions of the dome which are most susceptible to failure, complicated and expensive junction/hub connections are required at those places in the dome where structural members of different depths interconnect. This is especially true for large domes with concentrated loads at the center, such as sports arenas.
Theoretically, single network aluminum domes of this known kind can be used to span large distances, but as spans increase, so do the necessary size and commensurate cost of the struts which preferably are made by extrusion processes. Also, the large-section extrusions are produced in a limited number of places, leading to long lead times for order, delivery delays, and further increases in cost. Further, the size of structural shapes produced by the extrusion manufacturing process is limited. Specifically, aluminum extrusions can only be manufactured in depths up to 14 inches. In addition, aluminum has a low modulus of elasticity. These factors limit to approximately 450 ft. the span which single network aluminum dome structures built with struts of uniform sections can cover, and therefore, these circumstances effectively prevent domes of this kind from being used to enclose athletic stadia and the like where span distances on the order of 600 ft. or greater are required.
These considerations are magnified for sports arenas and other applications that require low profile or low rise covers (i e., shallow having low height). Thus, the maximum span of an aluminum single network low rise dome is smaller than 450 ft and buckling is a more serious problem. Single network low rise aluminum domes have been designed and built with spans up to 320 ft. in diameter, and these domes have approached the limits of the single network technology for low rise aluminum domes. To accentuate the problem, shallow domes are generally preferred over taller domes in most architectural applications, but because buckling is a more serious problem in shallow large diameter single network domes, single network aluminum extrusion domes are currently infeasible for many applications.
The most common mode of failure of single network low rise geodesic domes is called snap through buckling. In snap through buckling, the dome reverses curvature and cannot support applied loads over at least a portion of its area. Spherical domes and other curved structures are susceptible to snap through buckling. Unlike most structures, single network geodesic domes exhibit nonlinear geometric behavior. That is, as incremental load is applied, the incremental deflection of the structure becomes disproportionately larger. Snap through occurs when the structure is no longer capable of carrying load or the deflection of the structure becomes very large for a small incremental load. Such failure can occur when natural loads, such as wind, snow, or ice are added to design loads from lights, scoreboards, sound equipment, climate control equipment, cat walks, and other equipment suspended from the interior of the dome and the aggregate loads exceed the bucking capacity of the structure.
Construction of reticulated dome structures, i.e., domes in which the structural members are aligned along the lines of a network grid, can be performed using a large tower at a center opening in the structure; that opening may be closed later. An annular center portion of the structure is begun at (assembled around) the base of the tower and is attached to the top of the tower with hoist cables. When assembly of that initial top (central) portion of the dome is completed, it is raised upwardly by the hoist cables and the next portion (ring) of the structure is constructed at ground level as an outward extension of the annular central portion of the dome. This procedure is repeated until the structure is completed. This is a safe and efficient method for constructing a dome structure. However, when constructing a dome structure with a span of approximately 450 feet or greater, the height of the tower required to perform the erection becomes prohibitive, and this method of construction cannot be utilized.
Further, this method is impractical for structures with shapes other than spherical. Without the tower, the structures must be constructed by the attachment to the structure of one member at a time building slowly upward. This method can only be used for structures up to 250 ft in diameter and requires work in a dangerous environment high above ground level in mobile man-lifts to construct the entire structure. This approach also requires extensive shoring to prevent deformation of the structure during construction.
The foregoing circumstances demonstrate that a need exists for improved and efficient aluminum structural systems that can make use of aluminum extrusion technology to cover large sports arenas beyond approximately 450 ft. in span and which can utilize low profile designs for structures beyond approximately 400 ft. Further, benefit would be gained by using structural members which have a uniform cross sections. Further, there is a need for an efficient and safe method of constructing large aluminum reticulated dome structures and reticulated structures having non-spherical shapes. Thus, it is desirable to design and construct large span aluminum structural systems with aluminum members having the same depth throughout respective portions of the structure and to devise a safe method for constructing large structural systems with varying curvature.